Testing abnormality in the spatial arrangement of cells in the corneal endothelium using spatial point processes

The study of central corneal endothelium morphology is important in Ophthal mology. Some of the pathologies that could compromise endothelial cell morp hology are trauma, cataract, surgery, use of contact lenses, corneal dystro phies or degenerations. The quantitative analysis of cell shape and cellula r pattern is more sensitive in detecting subtle changes in endothelial morp hology than cell density measurement or cell area analysis. In this paper, the morphology of the central cornea, the most important area from the poin t of view of vision, is studied through an associated bivariate spatial poi nt pattern: the centroids of the cells and the triple points, that is, the points where three different cells converge. Nine different summary descrip tors (widely used in the statistical analysis of spatial point patterns) ha ve been used: the empty space distribution function; the nearest neighbour distribution function and Ripley's K-function for each type of point separa tely (centroids and triple points), plus the corresponding three versions o f these functions in the bivariate case. A control sample with similar age and cell density and no known abnormality is associated to each patient. Th e above descriptors are calculated for the patient and the controls. Each d escriptive of the patient is compared with the corresponding descriptors fr om the controls by means of a graphical analysis and a formal test. Some pa tients presenting different pathologies are analysed in detail. Endothelia considered morphologically abnormal by visual inspection, which were not de tected by hexagonality or density analysis, could be distinguished from con trol endothelia by these new descriptors. Copyright (C) 2001 John Wiley & S ons, Ltd.